Ultrasound system for high-speed and high resolution imaging applications

ABSTRACT

An ultrasound imaging system includes an array of ultrasound transducer elements chat send ultrasound energy into an object when energized for respective transmission time periods and provide responses to ultrasound energy emitted from the object for respective reception time periods, a reception modulation circuit modulating the responses with irregular sequences of modulation coefficients, a combiner circuit combining the modulated responses, and an image reconstruction processor configured to computer-process the combined modulated responses into one or more images of the object.

The patent application claims the priority of provisional application62/094,654 filed on Dec. 19, 2015.

TECHNICAL FIELD

This disclosure relates generally to ultrasound apparatuses and methodsfor obtaining an ultrasound image, and more particularly, to ultrasoundapparatuses and methods for obtaining a high-speed and high resolutionultrasound image.

BACKGROUND

Widely used medical imaging modalities can be broadly classified intothree categories based on the method of irradiation: (1) X-ray imaging;(2) radio frequency (RF) electromagnetic wave imaging; and (3) acousticpressure wave imaging. With respect to the first method, capturingX-rays leads to computed tomography (CT) imaging. With respect to thesecond method, excited water molecules emit RF waves, whose spatialquantities can be counted in magnetic resonance imaging (MRI). Moreover,with respect to the third method, the reflection of acoustic pressurewaves, typically at high audio frequencies, gives rise to ultrasound(US) imaging.

In addition to the field of medicine, these three imaging techniques areinvaluable for their non-invasive diagnostic contribution to geology,material testing, and other disciplines. Moreover, each of the threeimaging techniques has its own advantages and limitations. For example,CT imaging has the advantage of being able to yield high-resolutionpictures at relatively low cost. However, X-rays must be carefullyadministered because of detrimental cumulative effects. Thus, proper CTimaging uses the minimum amount of X-ray radiation necessary to obtain auseful picture, with due consideration to lifetime dosage limitations.In contrast, MRI is regarded as a safer alternative. However,maintaining MRI machines is considerably more expensive compared to CTmachines. Thus, the relatively higher cost associated with MRI prohibitsits use in casual diagnostics.

Ultrasound imaging is both safe and relatively inexpensive to use, andcan yield images with comparable quality as CT and MRI in certainimaging scenarios such as subcutaneous soft tissue imaging. For example,using ultrasound is the preferred way of imaging an unborn fetus becauseof its non-ionizing radiation and accessibility. However, conventionalultrasound imaging algorithms and sensor array geometries, as shown inFIG. 8, limit the overall frame rate and image quality defined in termsof resolution and signal-to-noise (SNR) ratio [1]. For example, theframe rate of a conventional B-mode (or 2D imaging) ultrasound system,where the images are generated one scan line at the time, isbottlenecked by the acoustic waveform propagation times [2]. In additionto the limited image acquisition speed, conventional ultrasound systemssuffer from sidelobe artifacts due to the focusing nature of theseimaging systems [1]. Another important limitation of conventionalultrasound systems is speckle noise arising from the coherent andunchanging illumination of the target medium [3]. Both speckle noise andsidelobes significantly limit imaging quality and resolution ofconventional ultrasound systems.

A variety of methods on improving the image quality, resolution, andspeed of conventional ultrasound systems have been proposed andexperimentally verified over the last five decades. These methods can bebroadly classified into three categories. The first category is focusedon adjusting the shape of the ultrasonic excitation pulse to increaseits effective bandwidth and applying an inverse filter on the receivedsignal (so called de-convolution) to improve image quality [3]-[7]. Thesecond group comprises methods based on improving the so-calledbeamforming function at the receive side to minimize imaging error[8]-[10]. The third and more recent category is focused on image datapost-processing to improve the resolution and image quality and reducecomplexity by taking advantage of sparsity of typical ultrasound image[11]-[17].

Even though successful in improving the image quality and resolution,these methods require significant hardware modifications and increase incost/complexity. For example, in all of these categories the core of theultrasound sensing array, as shown in FIG. 8, remains basicallyunchanged. That is, each element of the array remains equipped with acomplex chain of analog signal acquisition and data conversion blocks(digital-to-analog converter and power amplifier for acoustic pulsegeneration, as well as low-noise amplifier and analog-to-digitalconverter (ADC) for echo receiving), which does not favor portablebattery-operated implementations and further scaling to larger arrays.

Therefore, there is a need for an ultrasound imaging system where thehardware complexity is reduced and the speed of operation and the imagequality are increased.

Two lists of citation to references is included at the end of thisdisclosure, and the disclosure includes numbers in parenthesis thatrefer to the citations in Reference List A. Reference List B includesadditional citations. All of the cited references are herebyincorporated by reference in this disclosure.

SUMMARY

An object of the present disclosure is to provide an ultrasound imagingsystem and method.

In general, in one aspect, the present disclosure includes an ultrasoundsystem including an array of ultrasound transducer elements that sendultrasound energy into an object when energized for respectivetransmission time periods and provide responses to ultrasound energyemitted from the object for respective reception time periods, areception modulation circuit modulating the responses with irregularsequences of modulation coefficients, a combiner circuit combining themodulated responses, and an image reconstruction processor configured tocomputer-process the combined modulated responses into one or moreimages of the object.

The ultrasound imaging system may further include one or more of thefollowing features. The combiner circuit may be configured to combinethe modulated responses in the analog domain. The combiner circuit mayinclude at least two combiner channels each combining a respectivesubset of the responses. The reception modulation circuit may beconfigured to modulate the response with a sequence of pseudo-randommodulation coefficients. The reception modulation circuit may beconfigured to modulate the response with coefficients related to columnsof Hadamard matrices. The system may include a transmission modulationcircuit configured to select for energizing in each transmission periodonly plural-element subsets of the transducer elements that differbetween transmission time periods. The modulation circuit may beconfigured to energize only pseudo-randomly selected different subsetsof the transducer elements for different transmission time periods. Themodulation circuit may be configured to modulate the responses in theanalog domain with waveforms of positive and negative levels. Thecombiner circuit may include at least one amplifier having a positiveinput receiving the portions of the responses modulated with thepositive levels and a negative input receiving the portions of theresponses modulated with the negative levels of the modulatingwaveforms. The reconstruction processor may be configured to apply animaging matrix to the combined modulated responses to thereby generatethe one or more images of the object.

In general, in another aspect, the present disclosure includes anultrasound imaging system that includes a multi-element set ofultrasound transducer elements, an excitation pulse generator providinga succession of excitation pulses, a receiving switch matrix modulatingechoes received by the transducer elements with an essentially randomsequence of modulation coefficients, a circuit summing the modulatedechoes in the analog domain, and an image reconstruction processorconfigured to computer-process the summed modulated echoes into one ormore images of the object.

The ultrasound imaging system may further include one or more of thefollowing features. The receiving switch matrix may be configured tomodulate the echoes with modulating waveforms having irregular periods.The modulating waveforms may include waveforms of a succession ofpositive and negative levels. The system may include a differentialcharge amplifier, and the echoes modulated with the positive levels maybe supplied to a positive input and the echoes modulated with thenegative levels may be supplied to a negative input of the differentialamplifier. The image reconstruction processor may be configured to applyan image matrix to the summed modulated echoes to generate an image ofthe object. The image matrix may be selected to relate summed echoesfrom a known object to an expected image of the object generated withthe image reconstruction processor. The system may include ananalog-to-digital converter (ADC) converting the summed echoes into adigital sequence supplied to the image reconstruction processor. Thesystem may include a transmission switch matrix transmitting eachexcitation pulse only to a respective, essentially randomly selectedsubset of the elements in the set.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a model of an ultrasound imaging system used forcalculating Cramer-Rao Lower Bound;

FIG. 2 shows an ultrasound system according to an embodiment of thepresent disclosure;

FIG. 3 shows a block diagram of an integrated circuit, according to anembodiment of the present disclosure;

FIG. 4 shows an example of a waveform during the transmission phase.

FIG. 5 shows an example of modulation of received echo signals,according to an embodiment of the present disclosure;

FIGS. 6A-C show a comparison of ultrasound images from embodimentsdisclosed in this specification and a conventional ultrasound;

FIGS. 7A-C show a comparison of ultrasound images obtained according toexamples described in this specification; and

FIG. 8 shows a block diagram of a conventional ultrasound imagingsystem.

FIG. 9 shows a block diagram of a conventional B-mode ultrasound imagingsystem with parallel beamforming.

FIG. 10 shows a block diagram of an ultrasound system according to anembodiment of the present disclosure that employs a decompressionalgorithm to recover original transducer signals (or RF data) beforethey are passed to conventional beamforming algorithms such as forparallel beamforming.

DETAILED DESCRIPTION

This disclosure describes ultrasound imaging systems and methods. Indescribing examples and exemplary embodiments shown in the Figures,specific terminology may be employed for the sake of clarity. However,this disclosure should not be limited to the specific terminology soselected, and it should be understood that each specific elementincludes all technical equivalents that may operate in a similar manner.

FIG. 8 illustrates an example of a conventional ultrasound system. Ingeneral, early B-mode (or 2D imaging) ultrasound systems (e.g.,ultrasound systems developed in the 1960s) were entirely analog,including the beamforming function that performed the delay-and-sum (orelectronic focusing) operation. Because of advances with digitalcomputers, the analog scanning stages of the early B-mode ultrasoundsystems were replaced by digital components which improved imagereproducibility [18]. FIG. 8 shows that for each transducer, anindividual excitation pulse is generated, and the echo signal receivedfrom each point is received in a corresponding chain including ananalog-to-digital converter (ADC) and an amplifier.

FIG. 8 additionally shows that the early B-mode ultrasound systemscreate an image by measuring the echo signal power from one point at atime, while ignoring contributions from point scatterers that are offthe focal axis. This results in the loss of phase information across theelements of the array after the beamforming function. Accordingly,traditional ultrasound systems, such as the system of FIG. 8, can bedescribed as incoherent imaging systems.

Additionally, in general, in conventional ultrasound systems, such asthe system of FIG. 8, the spatial resolution is theoretically bounded byAbbe's diffraction limit (D_(Abbe)=λ/2NA), even in the absence of systemnoise, where λ is the wavelength of the excitation pulse, and NA is thenumerical aperture of the imaging system. With this theoretical limit,spatial resolution in ultrasound systems may be improved through the useof higher frequency ultrasonic waves, larger arrays, and/or use of somea priori knowledge about the imaged signal (such as sparsity).

In addition to Abbe's diffraction limit, other system parametersincluding, at least, noise and signal power play an important role inlimiting imaging resolution. Moreover, physical parameters of thetransducer array and imaging scenario set fundamental limits onultrasound systems.

This specification addresses ways to take advantage of the coherence ofthe received echo signals and to utilize the additional phaseinformation to improve imaging resolution dramatically with minimal orat least lesser need for additional electronics resources.

FIG. 1 illustrates an ultrasound imaging systems including a lineartransducer array of L transducer elements with spacing λ/2 illuminatinga target medium located along a central axis of the array at a distanceZ_(i). FIG. 1 shows that the target medium may be uniformly sampled witha spacing d. During a single observation the array transmits a finitelength plane-wave excitation pulse s(t) with wavelength λ and capturesdata from each sampling point with a reflectance coefficient a_(j). Theset of all reflectance coefficients represented as vector a=[a₁ a₂ . . .a_(M)]^(T) is a deterministic vector parameter to be estimated, whichrepresents the final ultrasound image of a target medium.

In some embodiments, received signals q_(k)(t) from the transducerelements (i.e., RF data) are combined into a single channel Q(t) bymeans of a linear function, H (i.e., the beamforming function). Inalternative embodiments, such as the embodiment of FIG. 1, for thepurpose of estimation error and resolution analysis the individualreceived signals q_(k)(t) may each be available to the imagereconstruction (or estimation) algorithm. In this manner, the effects ofthe linear function H on estimation error may be analyzed.

In one embodiment, such as the embodiment of FIG. 1, the fundamentallimits set by the physical parameters of the transducer array and theimaging scenario may be determined by finding a Cramer-Rao Lower Bound(CRLB) for estimation error. In the embodiment of FIG. 1, a contributorto error may be point scatterers in the azimuthal neighborhood (alongy-axis). In some embodiments, point scatterers at different rangedistances Z may also contribute to error. However, in the embodiment ofFIG. 1, point scatteres at different range distances Z may not beconsidered, because the propagation time difference between twoscatterers along the y-axis is orders of magnitude shorter than thepropagation time difference between two scatterers along z-axis due tothe far-field imaging assumption (i.e., distance Z_(i) is much greaterthan the array's aperture).

After a single plane-wave excitation s(t) transmitted by the array, thereceived sampled signal at the k^(th) element of the transducer arraymay be equal to,

q _(k)(nT _(s))=a ₁ s(nT _(s) −t _(1k))+ . . . +a _(M) s(nT _(s) −t_(Mk))+w(nT _(s))=s(nT _(s) ;a)+w(nT _(s))   (1)

where w(nT_(s)) are the samples of a zero-mean additive white Gaussian(AWG) noise, and t_(jk) is the propagation time from the scatterer at(z_(i),y_(i)) with reflectance coefficient a_(j) to the k^(th)transducer element.

Equation (2), defined below, may be used in connection with theultrasound imaging system of FIG. 1 in order to derive the CRLB for thevariance of the estimation error of reflectance parametersvar(â_(j)−a_(j)). In Equation (2), eSNR represents a Signal-to-Noiseratio (SNR) received by one element of the array, L is the number ofarray elements, p is the number of independent observations of theimaged tissue, d is the sampling grid spacing, and BW_(%) is thefractional bandwidth of the excitation pulse defined as the ratio of itseffective bandwidth and its center frequency f₀. Additionally,wavelength λ corresponds to the center frequency f₀ as λ=v_(s)/f₀, wherev_(s) is the speed of sound in the imaging medium.

$\begin{matrix}{{{var}\left( {{\hat{a}}_{j} - a_{j}} \right)} \geq {\frac{1}{{BW}_{\%} \cdot L \cdot p \cdot {eSNR}}\frac{D_{Abbe}}{d}}} & (2)\end{matrix}$

From the CRLB of the reflectance parameters, the fundamental limit onimage resolution d may be obtained, which may be shown in Equation (3)below. In Equation (3), CR is the contrast resolution (or peak imagingSNR) required by the imaging application.

$\begin{matrix}{{d({CR})} \geq {\frac{CR}{L \cdot p \cdot {eSNR}}\frac{D_{Abbe}}{{BW}_{\%}}}} & (3)\end{matrix}$

Equation (3) shows that it is possible to capture ultrasound images at asub-wavelength resolution (below Abbe's diffraction limit) although atthe expense of image quality (or reduced CR). Additionally, for the sameimaging system parameters (CR, NA, and BW_(%)), the imaging resolution dcan be improved by capturing more images to “average out” the systemnoise and increase the total SNR received by the array. The followingscenario illustrates the significance of this result.

For example, if f₀=600 kHz, BW_(%)=0.5, L=16, NA=0.2 (corresponding toan imaging depth of 5 cm), eSNR=15 dB, and p=10, then the Abbe'sdiffraction-limited resolution is about 2.5λ (6.2 mm). At the same time,the resolution limit from Equation (3) is equal to 0.03λ (or 78 μm) fora CR of 15 dB. Based on this, an ultrasound system that can preserve allthe information present in RF data should be, at least theoretically,capable of imaging with resolutions exceeding that of modern MRImachines (˜0.6 mm in [21]) at only a fraction of the equipment cost andimaging time [22]. For example, it has been shown that an ultrasonicpulse at 600 kHz can penetrate the human skull without significantattenuation [19]-[20]. The embodiment of FIG. 1 and correspondingequations show that the ultrasound system may be configured to preservethe information present in the RF data and further may be configured togenerate an image with increased resolution at an increased speed with alower cost of ultrasound system equipment.

In the embodiment of FIG. 1, Equation (3) represents a fundamental limiton the resolution of the ultrasound imaging system when estimatedreflectance parameters are non-zero and no a priori knowledge abouttheir statistics is available. In alternative embodiments, whereadditional information about the estimation parameters, including, butnot limited to, sparsity in some domain, may be available, there may bea further decrease in estimation error and improvements in resolution.

The fundamental limit on imaging resolution previously discussed wasderived assuming that signals from individual transducer elements areavailable. In most practical applications this is not realistic due tothe sheer volume of data (which may exceed GB/s). Therefore, in someembodiments, the RF data may be combined by means of a linear transformfunction H or beamforming function, where the channels arephase-delayed, weighted with an apodization window, and summed up into asingle channel Q(t). In general, the phase-delay operation can beignored since it is a reversible operation, with no effect on theinformation content and estimation error. Moreover, since theapodization window of traditional ultrasound imaging systems is usuallya low-pass spatial filter with filter coefficients that do not changeover different time samples, linear transformation function H can bedescribed as a linear time-invariant (LTI) transform. As such, thelinear transformation function H may cause loss of information at higherspatial frequencies, illustrated by a relatively poor resolution limitof 2-3λ in traditional ultrasound imaging systems.

In addition to reduced spatial resolution due to the focusing nature,another problem with traditional ultrasound system images is sidelobeartifacts, which appear as extraneous reflections from out-of-focusscatterers that are incorrectly interpreted as the signal along the mainfocusing axis [1]. In the embodiments of the present disclosure,sidelobe artifacts may be significantly reduced and even eliminated.

Returning the information obtained in RF data, there may be conditionsthat linear transformation function H must satisfy in order to preserveall the information available in RF data and not affect the estimationerror. First, since far-field imaging may be assumed, the azimuthalbandwidth (bandwidth along the y-axis) may be reduced 1/NA times withrespect to the range bandwidth (or z-axis). Therefore, since the signalsamples across the elements of the array at any given time instance areoversampled by a factor of 1/NA, they are highly correlated, occupyingonly a fraction of the available bandwidth. Accordingly, in someembodiments, one way of preserving all or most of the information is tospread the information across the frequency range defined by thesampling frequency (f_(s)). As long as the number of transducer elementsL is smaller than 1/NA, information from each of the elements can bemodulated to one of the non-overlapping spectral channels and no loss ofinformation is expected. Because linear transformation function H islinear, it must be time-varying to generate frequencies that are notpresent at its input.

Based on the discussion of FIGS. 8 and 1 and Equations (1)-(3), anultrasound imaging array equipped with a linear time-varying (LTV)beamforming function may be capable of achieving a sub-wavelengthimaging resolution, where the resolution can be readily traded for imagequality. Accordingly, embodiments of the present disclosure implement anLTV beamforming function, with a suitable excitation waveform, in anefficient manner and at affordable hardware costs.

For example, in some embodiments, a random modulation pre-integration(RMPI) function [23], where linear transformation function H isimplemented with mutually orthogonal pseudo-random vectors of 1's and−1's, may be configured to perform a spectral spreading operation. Thisenables simplification of the echo receive hardware to a switch matrixthat changes the polarity of signal samples from individual elements.Additionally, this enables simplification of the hardware such that onlyone summation amplifier and one ADC that operates at speeds comparableto the speed of one ADC in traditional ultrasound arrays may benecessary.

In embodiments of the present disclosure, the beamforming function ofthe ultrasound imaging system may be time-varying over different timeand spatial samples, uniformly spreading the information from differentpoint scatterers over each of the output signal samples (i.e., all pointscaterrers in the imaged medium are treated equally as opposed totraditional methods that focus at one scatterer at a time). This mayresult in a reconstructed ultrasound image that may exhibit reduced oreven eliminated sidelobe artifacts.

Embodiments of the present disclosure additionally provide improvementswith respect to speckle noise. In general, speckle noise arises frompoint scatterers that do not coincide with sampling grid points, anunavoidable issue in practical media. Speckles typically appear as afixed (although unpredictable) constructive/destructive interferencepattern due to coherent and unchanging illumination of the target medium[24]-[25]. The appearance of speckle noise can be reduced by averagingmultiple images of the same target at different illumination angles(i.e, an incoherent sum of multiple coherent images) [26]-[27]. Intraditional ultrasound imaging systems, where the target medium isusually illuminated with the same excitation waveform for one B-scanline at the time, the impossibility of repeated observations meansspeckle noise is a significant source of error. However, in embodimentsof the present disclosure, incoherent observations of coherent imagescan be readily implemented by selecting a random subset of arrayelements during a single target illumination, where the waveforms aretransmitted with the same phase. No additional hardware is necessarybecause this random selection can be implemented with the same switchmatrix used for beamforming.

Turning now to FIG. 2, an ultrasound imaging system is illustratedaccording to an embodiment of the present disclosure. In general, FIG. 2shows that received echo signals from the transducer elements, which maybe located on the identified piezoelectric film, may be modulated by anappropriate pseudo-random sequence and then summed up in the analogdomain, before they are passed through a single low-noise amplifier andADC. The excitation pulse (T_(x)) may be simultaneously provided to alltransducer elements selected for target illumination. As such,embodiments of the present disclosure may reduce the number of analogchannels in the imaging system (including low-noise amplifier, poweramplifier, ADC, and DAC) from one per array element to exactly one forthe entire array. This hardware simplification indicates a totalcomplexity and power reduction by a factor of L (typically 64-128),crucial in further developments of next generation battery-operated andportable US imaging systems. Furthermore, array geometries are no longercost-limited to linear arrays containing hundreds of elements. Instead,full 2D arrays for 3D imaging may be economically produced containingseveral thousand elements. In addition to scalability, the disclosedembodiment also processes images using unfocused signals received fromwhole-medium irradiation. Thus, the embodiments of the presentdisclosure may be able to acquire the whole-medium image using a single,pulsed transmission. This provides for a drastic acquisition time speedup compared to conventional B-mode US imaging. In addition, since it canreadily trade imaging speed for image quality, embodiments of thepresent disclosure provide imaging resolutions that may be close to thefundamental resolution limit, which is orders of magnitude higher thantypical resolution of conventional ultrasound systems (e.g., ˜0.1 mm vs.several millimeters) and comparable to that of modern MRI machines.These features may create new application opportunities such as 3Dreal-time heart imaging, deep tissue imaging, and even transcranialbrain imaging, which were not previously possible or practical withtraditional ultrasound systems. Moreover, because embodiments of thepresent disclosure use new computations for image reconstruction, theremay be a substantially lower complexity and cost of front-endelectronics. Therefore, when coupled with modern mobile platforms,including, but not limited to, tablets and smart phones, embodiments ofthe present disclosure may become genuinely portable.

More particularly, FIG. 2 illustrates a block schematic of an ultrasoundsystem according to an embodiment of the present disclosure. Asillustrated in FIG. 2, the system may include a 2D transducer array thatmay be fabricated as a piezoelectric film (such as PVDF) sandwichedbetween a grounded common electrode on one side and patterned electrodeson the other. The size of the patterned electrodes (˜λ/2 squared)determines the size of one transducer element.

The size of the transducer array may be any size known to those skilledin the art. For example, in one embodiment, a small size transducerarray consisting of 8×8 transducer elements with silver-coated patternedelectrodes each with the size of 1.24 mm2 (corresponding to 600 kHzexcitation frequency) may be procured from a piezoelectric filmsupplier. The transducer array may be bonded to a printed integratedcircuit board with a conductive epoxy for mechanical support andinterface to readout/driver electronics.

FIG. 3 illustrates a block diagram of an integrated circuit according toan embodiment of the present disclosure. As illustrated in FIG. 3, theintegrated circuit may include a memory block SRAM for modulationsequence storage, an on-chip low-noise charge amplifier, and poweramplifier PA, control and synchronization logic including a clock, aswell as an SPI interface for an off-chip access to the memory block. Theintegrated circuit may be designed and fabricated in any manner known tothose skilled in the art. For example, in some embodiments theintegrated circuit may be designed and fabricated via a high-voltageCMOS process, such as a 0.5 μm process.

FIG. 3 illustrates that the integrated circuit may additionally includea switch matrix. The switch matrix may be any device known to thoseskilled in the art including a set of devices for carrying out requisiteswitching with respect to each of the transducer elements on thetransducer array. For example, in the embodiment of FIGS. 2 and 3, theswitch matrix may include a plurality of modulation units. Eachmodulation unit may correspond to one of the transducer elements. Themodulation units may each contain one transmission gate (TG) for the Txphase and two TGs for the Rx phase. The TGs may be controlled by themodulation coefficients bTx and bRx, which are retrieved from a mainmemory block SRAM and temporarily stored in a small size (2-bit) memorybuffer of the modulation unit within one sampling period (˜200 ns).

During the excitation pulse transmission phase (Tx), an excitation pulsefrom the excitation pulse generator (FIG. 2) may first be converted toan analog signal (DAC) and amplified in a power amplifier (PA). Theoutput from the PA may then be modulated by a modulation signal withmodulation coefficients b_(ij)(t), which may be constant during theentire length of the excitation pulse. In some embodiments, themodulation coefficients may be either 1 or −1. Alternatively, in someembodiments, such as the embodiment of FIG. 2, the modulationcoefficients may be equal to either 1 or 0, which may be implemented asa switch matrix and fed to a subset of transducer elements. That is, inthe embodiment of FIG. 2, a pseudo-randomly selected subset oftransducer elements may be an array selected by modulation coefficientsof zero and plus unity values, where a zero value means that arespective transducer element is not energized for a given transmissiontime period, and a plus unity value means the element is energized forthat transmission time interval, and where the array of (0, 1) values isselected with some degree of randomness from one transmission timeinterval to another, such as based on Hadamard matrices, a pseudo-randomgenerator, or some other source known to those skilled in the art. Insome embodiments the subset of transducer elements may be all of thetransducer elements. Alternatively, in some embodiments, the subset oftransducer elements may be more than one, but less than all of thetransducer elements, e.g., one-half of the transducer elements.

FIG. 4 illustrates an example of the excitation pulse (Tx) as applied toa pseudo-random subset of transducer elements, according to anembodiment of the present disclosure. As shown in FIG. 4, a singleexcitation pulse (illustrated to the left of the transducer elements)may be generated. Each modulation unit (x) in the integrated circuit,which corresponds to a transducer element, may be configured to modulatethe excitation pulse. In the embodiment of FIG. 4, the modulation units(x) may be modulating the excitation pulse with a coefficient b_(ij) of0 or 1. As such, the excitation pulse may be transmitted only to thesubset of transducer elements corresponding to a modulation coefficientof 1 as illustrated.

After transmission of the excitation pulse to the subset of transducerelements, echo signals are received. During the echo receive operation(Rx), received signals from transducer elements are modulated via thecorresponding modulation unit (x) with b_(ij)={−1,1}. The modulationsignals b_(ij)(t) may be square waves with amplitude changing between 1and −1 (i.e., these changing amplitudes act as the modulationcoefficients). The modulation coefficients b_(ij) may be chosen in apseudo-random manner with a period less than or equal to the samplingperiod T_(s)=1/f_(s). Alternatively, the modulation coefficients may bechosen as elements of mutually orthogonal vectors (e.g., first L vectorsof N×N Hadamard matrix).

After the received echo signals are modulated, they may be summed up ina low-noise charge amplifier. FIG. 5 illustrates an example ofmodulation and summation of received echo signals from the subset oftransducer elements. As shown in FIG. 5, each echo signal received froma transducer element may be modulated by a corresponding squaremodulation wave having modulation coefficient values of 1 or −1. Themodulated echo signals may be summed as they pass through a summationnode and charge amplifier.

Returning to FIG. 2, the summed output from the charge amplifier may beconverted to digital form using an analog-to-digital converter (ADC) andpassed to an image reconstruction module operating according to areconstruction algorithm. The image reconstruction can be implemented oneither a local computational engine or on remote cloud computing serversfor further power and form factor reduction.

In embodiments of the present disclosure, several methods may beimplemented for reconstructing (or decoding) the computationalultrasound image from the signal channel Q(t). In some embodiments, thesignal Q(t) after the sampling operation and analog-to-digitalconversion can be described as a pN×1 vector signal Q=[Q¹(0) . . .Q¹((N−1)T_(s)) Q²(0) . . . Q²((N−1)T_(s)) . . . Q^(p)(0) . . .Q^(p)((N−1)T_(s))]^(T), where the sample Q^(i)(nT_(s)) represents asignal sample at time instant nTs during the i^(th) observation, p isthe total number of independent observations, and N is the total numberof samples during a single observation.

The received signal vector Q can be described in matrix notation as inEquation (4), identified below, where the known imaging matrix Πrepresents a combination of transmitted excitation waveform matrix,propagation matrix, and beamforming function, vector A is a columnvector of reflectance coefficients a_(ij), and W is a column vector ofAWG noise samples.

Q _(pN×1)=Π_(pN×M) A _(M×1) +W _(pN×1)  (4)

The imaging matrix Π of size pN by M, where M is the total number ofimaged sampling grid points, contains a total of p submatrices Π^(j) ofsize N by M each corresponding to one of the observations as shown belowin Equation (5).

$\begin{matrix}{\Pi_{pNxM} = \begin{bmatrix}\Pi_{NxM}^{1} \\\vdots \\\Pi_{NxM}^{p}\end{bmatrix}} & (5)\end{matrix}$

In some embodiments of the ultrasound imaging system, the submatricesΠ^(j) are precalculated and stored in memory for a given excitationpulse, set of transmission and receive modulation coefficients, andsampling grid locations. Assuming a non-dispersive imaging target, the(n+1,k) element of the submatrix Π^(j) can be calculated, for example,as in Equation (6), identified below, where 0≦n≦N−1 and 1≦k≦M.

The R_(s)(0) term in Equation (6) is the energy of the transmittedexcitation pulse s(t). [H^(j)]_(n+1,i) is the modulation coefficientcorresponding to the n+1^(th) time sample and i^(th) transducer elementduring the echo receive operation of the j^(th) observation. Γ^(jm) isthe transmission modulation coefficient corresponding to the j^(th)observation and m^(th) transducer element. s′(t) is the normalizedexcitation pulse transmitted by the transducers. T_(s) is the samplingperiod and t_(mki) is the round-trip propagation delay from the m^(th)transducer to the k^(th) sampling grid point and back to the i^(th)transducer. r(t_(mki)) is the propagation loss along the propagationdistance equal to v_(s)t_(mki). The constant time delay Δ and the totalnumber of samples N are chosen such that the reflected echo signals fromall of the sampling grids points are entirely received with the minimalnumber of samples (i.e., Δ≦min(t_(mki)) andN≧(max(t_(mki))−Δ+T_(p))/T_(s), where T_(p) is the duration of theexcitation pulse s(t)).

[Π^(j)]_(n+1,k)=√{square root over (R _(s)(0))}Σ_(i=1) ^(L) [H^(j)]_(n+1,i)Σ_(m=1) ^(L)Γ_(m) ^(j) s′(nT _(s) +Δ−t _(mki))r(t_(mki))  (6)

The precalculated matrices Π^(j) are then used to form the imagingmatrix Π, which is then stored in a memory of the image reconstructionmodule for image decoding purposes. In another embodiment of thecomputational ultrasound imaging system, the imaging matrix Π may beestimated (instead of precalculated) by imaging a known target.

Given the imaging matrix Π and received signal vector Q, vector A can beestimated by using convex optimization algorithms. In one embodiment ofthe ultrasound imaging system, decoding is based on a linearleast-squares (LS) minimum variance estimator Â_(M×1), whose estimationerror is equal to the CRLB previously discussed, which is shown inEquation (7), where θ represents a reconstruction or decoding matrix.The corresponding covariance matrix of the estimator is shown below inEquation (8).

$\begin{matrix}{\mspace{79mu} {{\hat{A}}_{M\; x\; 1} = {{\left( {\Pi^{T}\Pi} \right)^{- 1}\Pi^{T}Q_{{pNx}\; 1}} = {\Theta \; Q_{{pNx}\; 1}}}}} & (7) \\{C_{A} = {{\frac{1}{p}{I^{- 1}(A)}} = {{E\left\lbrack {\left( {\Pi^{T}\Pi} \right)^{- 1}\Pi^{T}{WW}^{T}{\Pi \left( \left( {\Pi^{T}\Pi} \right)^{- 1} \right)}^{T}} \right\rbrack} = {\sigma^{2}\left( {\Pi^{T}\Pi} \right)}^{- 1}}}} & (8)\end{matrix}$

Since Π and θ are constant for a given system and imaging scenario, theimage reconstruction is implemented as a single matrix multiplicationbetween θ and the received vector Q_(pN×1).

FIGS. 6A-C show preliminary simulation results using Field II acousticpackage in MATLAB [28]. FIGS. 6A-C compare ultrasound images obtainedfrom embodiments disclosed herein (FIG. 6B) at λ/8 resolution withconventional ultrasound images (FIG. 6C) of a hyperechoic cyst with adiameter of 1.5λ in a speckle background with density of 10 scatterersper square wavelength (FIG. 6A). As shown in FIG. 6B, the ultrasoundsystem is able to distinguish between the cyst and backgroundscatterers, while the image obtained by the conventional ultrasound(FIG. 6C) exhibits a strong speckle noise without a clear view of thecyst region. Accordingly, FIGS. 6A-C confirm that the ultrasound systemdescribed herein is capable of achieving sub-wavelength resolution,while reducing the sidelobe artifacts and speckle noise.

Moreover, as previously discussed, further improvements in theresolution and/or image quality are expected if there is moreinformation available about the estimated parameters such as sparsity insome domain (e.g., either spatial or frequency domain) [11]-[12].Accordingly, in some embodiments of the ultrasound imaging system, theimage decoding algorithm may be utilizing an additionalsparsity-promoting L1-norm regularized cost as described in Equation(9), identified below, where α is a sparsity-controlling parametertypically chosen via cross-validation [29]-[30].

FIGS. 7A-C illustrate a comparison between the images obtained fromembodiments of the ultrasound system disclosed herein utilizing thesparsity-agnostic LS estimation method as described in Equation (7) andthe method described in Equation (9). FIG. 7A shows a 1.5λ diameterhypoechoic cyst in a speckle background. FIG. 7B shows the cyst of FIG.7A imaged utilizing the least-square estimation method. FIG. 7C showsthe cyst of FIG. 7A imaged utilizing addition L₁-norm cost for eSNR=6dB, L=32, range distance of 9 cm, and f₀=2 MHz, and d=λ. As expected,the signal adaptive method that leverages a priori knowledge about thereflectance field, results in enhanced de-noising with a consequentreduction in estimation error and improved contrast resolution.

$\begin{matrix}{{{\hat{A}}_{M\; x\; 1} = {\underset{A_{M\; x\; 1}}{argmin}\left\{ {{{Q_{{pNx}\; 1} - {\Pi_{pNxM}A_{M\; x\; 1}}}}_{2} + {\alpha {A_{M\; x\; 1}}_{1}}} \right\}}},{{s.t.\mspace{14mu} {- 1}} \leq A_{{Mx}\; 1} \leq 1}} & (9)\end{matrix}$

Even though the minimum variance image reconstruction in Eq. (7) entailsa single matrix multiplication, it may still pose a challenge forreal-time (e.g., 30 frames/sec) ultrasound imaging on mobile platforms.Also, if some of the acquisition-system conditions change, then so doesthe reconstruction matrix θ and one needs to solve a large-scaleoverdetermined LS problem again. To ensure the computational loadremains at an affordable level, the dimensionality of the problemsdefined in Equations (7) and (9) may be reduced while guaranteeing acontrollable penalty in estimation error. This way, the computationalload (or imaging speed) can be efficiently traded for image quality asallowed and/or required by a specific imaging application.

Going back to the potentially highly overdetermined (pN

M) LS image reconstruction task in Equation (7), randomized numericallinear algebra may be used to discard all but the most informativesubsets of measurements in Q_(pN×1), based on (random) subsampling ordata sketching [31]-[32]. The target number of measurements retained isa function of the desired image quality, real-time constraints, and theavailable computational budget. The basic premise of the data sketchingtechniques is to largely reduce the number of rows of and prior tosolving the LS problem in Equation (5), while offering quantifiableperformance guarantees of the solution to the reduced problem [33]. Adata-driven methodology of keeping only the “most” informative rowsrelies on the so-termed (statistical) leverage scores, which are thenused to define a sampling probability distribution over the rows of θ.Remarkably, results in [33] assert that performance of leveragescore-based sampling degrades gracefully after reducing the number ofequations. Unfortunately, their complexity is loaded by the leveragescores computation, which, similar to [34], requires SVD computations—acumbersome (if not impossible or impractical) task for cases where M andNp are large. One can avoid computing the statistical leverage scores bypre-multiplying θ and Π with a suitable random Hadamard transform, andthen uniformly subsampling a reduced number of rows [33].

With regards to Equation (9) being convex, iterative solvers areavailable including interior point methods and centralized onlineschemes based on (sub)gradient based recursions [35]. For big datahowever, off-the-shelf interior point methods may be too demandingcomputationally, and are not amenable to decentralized or parallelimplementations [33]. Subgradient-based methods are structurally simplebut are often hindered by slow convergence due to restrictive step sizeselection rules. To address these issues, real-time algorithms asdescribed in [36-39] could be used for L1-norm minimization described inEquation (9). These algorithms offer great promise for imaging systems,especially for situations in which measurements are stored in the cloud,or, are streamed in real time and decoding must be performed“on-the-fly” as well as without an opportunity to revisit pastmeasurement [40].

In terms of the computation involved for image reconstruction, theultrasound system disclosed herein allows flexible, controlled tradeoffbetween computation costs and some quality factor. In one embodiment, aportable system uses low-power hardware which works for a hand-helddevice with a lower image resolution display. In another embodiment, thecomputation algorithm and implementation can be dynamically adjusted tofavor speed over image quality, for instance, during video mode andprovide slower computation for still image of a higher resolution andimage quality. This provides a smooth video mode with optional pause andzoom/enhance option.

While general-purpose computers are flexible when implementing anycomputation algorithms, the price for this flexibility is the (sometimesextremely) low efficiency. There are a variety of special purposeaccelerators. Matrix multiplication is a common target of acceleration,though memory bandwidth tends to be an issue limiting FPGA styleaccelerators [41-44]. The image reconstruction of the ultrasound systemlends itself to a special purpose accelerator design, where numericalcalculations need not conform to industry standards usually designed tobe general purpose. For example, instead of a fixed precision such asdouble-precision floating-points, a number of increasingly simplifiedoptions will be embodiments of this design style: (1) special floatingpoint representation with custom mantissa and exponent, especiallyallowing for de-normal representation to simplified hardware, (2)reduced operand width such as half-precision floating-point, and (3)fixed-point (including integer) representation. Another embodiment ofspecial accelerator support is dynamic reconfiguration between differentembodiments as listed above. A final embodiment exploits the sparsity toreduce communication and computation demands. All these designs canimprove cost, energy, and portability with negligible or acceptableimpact on some figure of merit of the resulting image or video.

Further to the discussion with respect to FIG. 1, the following is adetailed derivation of the CRLB for the variance of the estimation errorand imaging resolution of the conventional ultrasound imaging systemshown in FIG. 1.

After a single plane-wave excitation s(t) transmitted by the array, thereceived signal at the k^(th) element of the transducer array is equalto,

q _(k)(t)=a ₁ s(t−t _(1k))+a ₂ s(t−t _(2k))+ . . . +a _(M) s(t−t_(Mk))+w(t)  (10)

where w(t) is a zero-mean additive white Gaussian (AWG) noise, tjk isthe propagation time from the scatterer at (zi,yi) with reflectancecoefficient a_(j) to the k^(th) transducer element. After the samplingoperation, the received signal can be represented as in Equation (11),shown below, where n=0, 1, . . . , N−1. The total number of samples N ischosen large enough so that the waveforms from all the point scatterersare entirely received.

q _(k)(nT _(s))=a ₁ s(nT _(s) −t _(1k))+ . . . +a _(M) s(nT _(s) −t_(Mk))+w(nT _(s))=s(nT _(s) ;a)+w(nT _(s))   (11)

The vector of reflectance coefficients a=[a₁ a₂ . . . a_(M)]^(T) is adeterministic vector parameter to be estimated. From Equation (11), wesee that the estimation of a belongs to a class of linear estimationproblems in the presence of AWG noise. The CRLB for the estimation errorof the parameters a_(i) can be calculated as in Equation (12), shownbelow, where I(a) is the Fisher information matrix of the signalreceived by the entire array and [·]_(ij) indicates j^(th) diagonalelement. Since the received signals at different elements of the arrayare independent observations of a, the Fisher information matrix of thearray can be represented as the sum of Fisher information matrices ofthe individual transducer elements. The observations are independent andmay be repeated p times, reducing the error by a factor of p.

$\begin{matrix}{{{{var}\left( {{\hat{a}}_{j} - a_{j}} \right)} \geq {\frac{1}{p}\left\lbrack {I^{- 1}(a)} \right\rbrack}_{jj}} = {\frac{1}{p}\left\lbrack \left( {\sum\limits_{k = 1}^{L}{I_{k}(a)}} \right)^{- 1} \right\rbrack}_{jj}} & (12)\end{matrix}$

The elements of the Fisher information matrix of the individualtransducer channels can be calculated as in Equation (13), shown below,where σ² is the total noise power within the sampling bandwidthf_(s)=1/T_(s).

$\begin{matrix}{\left\lbrack {I_{k}(a)} \right\rbrack_{ij} = {{\frac{1}{\sigma^{2}}{\sum\limits_{n = 0}^{N - 1}{\frac{\partial{q_{k}\left( {nT}_{s} \right)}}{\partial a_{i}}\frac{\partial{q_{k}\left( {nT}_{s} \right)}}{\partial a_{j}}}}} = {\frac{1}{\sigma^{2}}{\sum\limits_{n = 0}^{N - 1}{{s\left( {{nT}_{s} - t_{i}} \right)}{{s\left( {{nT}_{s} - t_{j}} \right)}.}}}}}} & (13)\end{matrix}$

If we assume that the sampling period is small enough, the summationterm in Equation (13) can be expressed in terms of normalizedautocorrelation function of the excitation waveform R′_(s)(τ) andecho-SNR (eSNR) defined as the ratio of the excitation waveform energyR_(s)(0) and the noise power spectral density N₀=σ²T_(s).

$\begin{matrix}{\left\lbrack {I_{k}(a)} \right\rbrack_{ij} = {{\frac{1}{\sigma^{2}T_{s}}{R_{s}\left( {t_{i} - t_{j}} \right)}} = {{\frac{R_{s}(0)}{\sigma^{2}T_{s}}{R_{s}^{\prime}\left( {t_{i} - t_{j}} \right)}} = {{eSNR}*{R_{s}^{\prime}\left( {t_{i} - t_{j}} \right)}}}}} & (14)\end{matrix}$

If we now assume that the point-scatterers are in the far-field, theelements of the Fisher information matrix can be calculated as inEquation (15), where NA is the numerical aperture, d′ is the samplinggrid spacing (or resolution) normalized to the wavelength of theexcitation waveform, f₀ is the center frequency of the excitationwaveform, L is the total number of array elements, and M is the numberof observed grid points along the y-axis at the radial distance z_(i).

$\begin{matrix}{{\left\lbrack {I_{k}(a)} \right\rbrack_{ij} = {{eSNR}*{R_{s}^{\prime}\left( {\left( {j - i} \right)\frac{{NAd}^{\prime}}{f_{0}\left( {L - 1} \right)}\left( {{2k} - 1 + {2{d^{\prime}\left( {M - \left( {i + j - 1} \right)} \right)}}} \right)} \right)}}},\mspace{20mu} {k = 1},2,{{\ldots \mspace{14mu} L};i},{j = 1},2,{\ldots \mspace{14mu} M}} & (15)\end{matrix}$

A goal is to determine the relationship between the estimation errorvar(â_(j)−a_(j)) and the imaging system parameters such as NA,resolution d, eSNR, and bandwidth of the excitation waveform. Eventhough the Fisher information matrix I(a) is a real-symmetric Toeplitzmatrix, finding an analytical form for the j^(th) diagonal element ofits inverse is a non-trivial task in general. Assuming that theexcitation signal is a finite length (K-cycles) sinusoidal waveform withfrequency f₀ and period T as in Equation (16), the normalizedautocorrelation function of the excitation signal is calculated inEquation (17). Also, the fractional bandwidth BW_(%) of the excitationwaveform is shown in Equation (18), where BW_(RMS) is itsroot-mean-squared bandwidth, vs is the speed of sound in the imagingmedium, and λ=v_(s)/f₀.

$\begin{matrix}{\mspace{79mu} {{s(t)} = \left\{ \begin{matrix}{{\sin \left( {2\pi \; f_{0}t} \right)},} & {{{- {KT}}/2} \leq t \leq {{KT}/2}} \\{0,} & {otherwise}\end{matrix} \right.}} & (16) \\{{R_{s}^{\prime}(t)} = \left\{ \begin{matrix}{{{\left( {1 - \frac{t}{KT}} \right){\cos \left( {2\pi \; f_{0}t} \right)}} + {\frac{1}{4\pi \; K}{\sin \left( {2\pi \; f_{0}t} \right)}}},} & {{- {KT}} \leq t \leq {KT}} \\{0,} & {otherwise}\end{matrix} \right.} & (17) \\{\mspace{79mu} {{BW}_{\%} = {\frac{{BW}_{{RM}\; S}}{f_{0}} = {\frac{{BW}_{{RM}\; S}\lambda}{v_{s}} = \frac{1}{2K}}}}} & (18)\end{matrix}$

Given the normalized autocorrelation function from Equation (17), thediagonal elements of the inverse Fisher information matrix I⁻¹(a) can benumerically calculated. It can be shown that the diagonal elementcorresponding to the center grid point (z_(i),y_((M+1))/2) dominatesother terms indicating maximum estimation error. For this reason,attention may be focused to this worst-case scenario.

Using curve fitting we show that the CRLB associated to the center gridpoint (z_(i),y_((M+1)/)2) can be expressed as in Equation (19), whereaSNR=L*p*eSNR represents a total SNR received by the array during pobservations, D_(Abbe) is the Abbe diffraction limit of the imagingsystem defined as λ/2NA, and S_(r) is the range resolution defined asv_(s)/2BW_(RMS).

$\begin{matrix}{{{{var}\left( {{\hat{a}}_{j} - a_{j}} \right)} \geq \frac{K \cdot \lambda}{L \cdot {NA} \cdot d \cdot p \cdot {eSNR}}} = {{\frac{1}{{BW}_{\%} \cdot {aSNR}}\frac{D_{Abbe}}{d}}==\frac{S_{r}}{{NA} \cdot d \cdot {aSNR}}}} & (19)\end{matrix}$

Since the reflectance coefficients a_(i) assume values in the range of[−1, 1], the peak imaging SNR, often referred to as Contrast Resolution(CR), can be defined as

${pSNR} = {\frac{{\max \left( a_{j} \right)}^{2}}{{var}\left( {- a_{j}} \right)} = {1/{{{var}\left( {{\hat{a}}_{j} - a_{j}} \right)}.}}}$

From the CRLB of the reflectance parameters, one can readily obtain thefundamental limit on image resolution d, as shown in Equation (20).

$\begin{matrix}{{{d({CR})} \geq {\frac{CR}{aSNR}\frac{D_{Abbe}}{{BW}_{\%}}}} = {\frac{CR}{aSNR}\frac{S_{r}}{NA}}} & (20)\end{matrix}$

In order to achieve spatial resolutions below diffraction limit with animaging system of the type described above, the transducer array shouldhave a dimensionality that is one less than the dimensionality of animaged object (i.e., to image a 3D object, the transducer elements mustbe arranged in a 2D array). Otherwise, if a 1D transducer array is usedto image 2D slices of a 3D object, the spatial resolution of the systembecomes limited by the so-called elevation resolution, which is definedby the diffraction limit of an acoustic lens used for beam confinementin the elevation direction (i.e., the resolution becomes limited by thebeam-width in the elevation direction). Therefore, if an imaging systemequipped with a 1D array is used to image 3D objects, no major spatialresolution improvement is expected over the traditional 2D US systems.Even though recent developments in device manufacturing promise betterscalability and ability for mass production of less expensive 2D arrays,their manufacturing cost still remains high with respect to the presentstate of technology. Therefore, the majority of commercially availableB-mode US systems are believed to be 2D systems employing 1D arrays.Nevertheless, even if the embodiments described in this disclosure use1D transducer arrays rather than 2D arrays may not be able to achievesub-wavelength resolution in the elevation direction, theirpseudo-random beamforming function may still be utilized tosignificantly reduce the complexity of the traditional 2D US systems. Inaddition, the pseudo-random apodization (or pseudo-random selection oftransducer elements) during the pulse transmission, as described above,promises a significant reduction of the sidelobe artifacts and specklenoise.

FIG. 9 depicts a block schematic of a typical B-mode US system utilizingparallel beamforming. Similar to the traditional B-mode US, each channelis equipped with a complex signal processing chain (e.g., low-noiseamplifier A, A/D converter ADC, and a respective beam forming circuitpath for each of the transducers), which does not favor portablebattery-operated implementations and further scaling to larger arrays.

Parallel beamforming methods commonly use a plane-wave excitation toilluminate imaged object and then record returned echoes from all of theelements of the array (RF data). The RF data is then passed to the imagereconstruction algorithm that performs beamforming (e.g., delay-and-sum)for each scan line in parallel. This operation is performed in digitaldomain, so that the overall imaging speed is independent of the numberof scan lines and the frame rates may exceed that of traditional B-modeUS systems by two orders of magnitude.

As depicted in FIG. 10, in one embodiment of the present disclosure thereceived echo signals from each of the transducers in the array aremodulated with a pseudo-random sequence of 1's and −1's by a modulatingswitch matrix (X) before they are summed up into a single channel by acombiner circuit labeled summation amplifier. The resulting analogsignal is then converted to digital form by an ADC circuit and stored ina memory and/or wirelessly or otherwise transmitted to a host computerfor image reconstruction by a decompression and RF signal reconstructionmodule that feeds its output into a parallel beamformer generatingimages of the target. Due to a much reduced channel count achieved bythe compressive nature of pseudo-random beamforming (or modulation with1's and −1's), the total data produced by the transducer array during asingle target illumination and subsequent signal acquisition issignificantly reduced as compared to traditional B-mode US systems,which permits more compact designs with reduced memory size and/ornetwork throughput requirements. In this embodiment of the presentdisclosure, the highly compressed single channel data after themodulation and combining operation is passed to a “decompression”algorithm that recover the RF data before it is subjected to atraditional beamforming techniques such parallel beamforming algorithm.A variety of decoding/optimization algorithms such as constrainedleast-squares (LS) estimation algorithm and L1-norm minimizationalgorithm can be used for decompression algorithm implementation. Thefollowing equation describes a constrained LS algorithm that may be usedto recover highly oversampled RF data qL×N,

$\begin{matrix}{{{\hat{q}}_{LxN} = {\underset{q_{LxN}}{argmin}\left\{ {{Q_{{Nx}\; 1} - {{diag}\left( {H_{NxL}q_{LxN}} \right)}}}_{2} \right\}}},{{{s.t.\mspace{14mu} W_{LxL}^{1}}{\hat{q}}_{LxN}W_{NxN}^{2}} = {\alpha \; {\hat{q}}_{LxN}}}} & (21)\end{matrix}$

where Q_(N×1) is the received single channel data, H_(N×L) is the LTVbeamforming matrix, W¹ _(L×L) is the band-limitation matrix across thetransducer array elements, and W² _(N×N) is the band-limitation matrixacross the time samples. After the decompression step, the estimated RFdata may then be passed to a conventional parallel beamforming engine tocalculate reflectance coefficients (or brightness) of the imaged target.

Typical parallel beamforming systems utilize plane-wave excitation fortissue (target) illumination, where all transducer elements aresimultaneously pulsed. As described in the literature, the plane-waveillumination associated with parallel beamforming systems may result insignificantly increased side-lobe artifacts as compared to traditionalB-mode US systems, which predominantly utilize focused pulse excitation.To mitigate the side-lobe artifacts, a pseudo-random pulse excitation ofthe type the embodiments of this disclosure employ may be used. Forexample, during a single target illumination, a random subset of thetransducer array elements will be selected for target illumination. Eachselected element would transmit the same phase excitation pulse and thetarget illumination will be repeated each time with a different randomlyselected subset of transducer elements. Due to this additional diversityprovided by this “randomized apodization” on the transmission, it isexpected that the sidelobe artifacts will be reduced after repeatedtarget illumination and subsequent averaging of individual B-modeframes. For the same reason, it is expected that the speckle noise maybe significantly reduced. It should be noted that this pseudo-randomapodization on pulse transmission only requires a simple switch matrixfor its implementation without adding much complexity to the analogfront-end.

The embodiments and examples above are illustrative, and many variationscan be introduced to them without departing from the spirit of thedisclosure or from the scope of the appended claims. For example,elements and/or features of different illustrative and exemplaryembodiments and figures herein may be combined with each other and/orsubstituted with each other within the scope of this disclosure. Theobjects of the invention, along with various features of novelty, whichcharacterize the invention, are pointed out with particularity in theclaims annexed hereto and forming a part of this disclosure. For abetter understanding of the invention, its operating advantages and thespecific objects attained by its uses, reference should be made to theaccompanying drawings and descriptive matter.

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B., “Speckle in ultrasound B-mode scans,” Sonics    and Ultrasonics, IEEE Transactions on, vol. 25, no. 1, pp. 1, 6,    January 1978.-   [26] Ouyang, G. “Laser speckle reduction based on angular diversity    induced by Piezoelectric Benders,” JOURNAL OF THE EUROPEAN OPTICAL    SOCIETY-RAPID PUBLICATIONS, ISSN 1990-2573, 2013, Vol. 8, p. 4.-   [27] M. N. Akram, Z. Tong, G. Ouyang, X. Chen, and V. Kartashov,    “Laser speckle reduction due to spatial and angular diversity    introduced by fast scanning micromirror,” Appl. Optics 49(17),    3297-3304 (2010).-   [28] J. A. Jensen, “FIELD: a program for simulating ultrasound    systems,” in 10th Nordicbaltic Conference on Biomedical Imaging,    Supplement 1, Part 1, vol. 34, 1996, pp. 351-353.-   [29] T. Hastie, R. Tibshirani, and J. Friedman, The Elements of    Statistical Learning, 2nd ed. New York: Springer, 2009.-   [30] R. Tibshirani, “Regression shrinkage and selection via the    lasso,” J. Roy. Stat. Soc. B, vol. 58, pp. 267-288, 1996.-   [31] M. W. Mahoney, “Randomized algorithms for matrices and data,”    Foundations and Trends in Machine Learn., vol. 3, no. 2, pp.    123-224, 2011.-   [32] K. L. Clarkson and D. P. Woodruff, “Low rank approximation and    regression in input sparsity time,” in Proc. Symp. Theory Computing,    Jun. 1-4, 2013, pp. 81-90.-   [33] K. Slavakis, G. B. Giannakis, and G. Mateos, “Modeling and    optimization for Big Data analytics,” IEEE Signal Processing    Magazine, vol. 31, no. 5, pp. 18-31, September 2014.-   [34] V. M. Patel, H. V. Nguyen, and R. Vidal, “Latent space sparse    subspace clustering,” in Proc. of Intl. Conf. Computer Vision,    Sydney: Australia, 2013.-   [35] S. Shalev-Shwartz, “Online learning and online convex    optimization,” Foundations and Trends in Machine Learning, vol. 4,    no. 2, pp. 107-194, 2012.-   [36] M. Mardani, G. Mateos, and G. B. Giannakis, “Dynamic    anomalography: Tracking network anomalies via sparsity and low    rank,” IEEE Journal of Sel. Topics in Signal Processing, vol. 8,    February 2013.-   [37] M. Mardani, G. Mateos, and G. B. Giannakis, “Decentralized    sparsity-regularized rank minimization: Algorithms and    applications,” IEEE Trans. on Signal Processing, vol. 61, pp.    5374-5388, November 2013.-   [38] G. Mateos, J. A. Bazerque, and G. B. Giannakis, “Distributed    sparse linear regression,” IEEE Trans. Signal Processing, vol. 58,    no. 10, pp. 5262-5276, October 2010.-   [39] G. Mateos, I. D. Schizas, and G. B. Giannakis, “Distributed    recursive least-squares for consensus-based in-network adaptive    estimation,” IEEE Transactions on Signal Processing, vol. 57, no.    11, November 2009.-   [40] K. Slavakis, S.-J. Kim, G. Mateos, and G. B. Giannakis,    “Stochastic approximation vis-a-vis online learning for Big Data,”    IEEE Signal Processing Magazine, vol. 31, no. 6, pp. 124-129,    November 2014.-   [41] F. Bensaali, A. Amira, R. Sotudeh, “Floating-point matrix    product on FPGA”, Proc. IEEE/ACS Int. Conf. on Computer Systems and    Applications, pp. 466-473, 2007.-   [42] C. Y. Lin, H. K.-H. So, P. H. Leong, “A model for matrix    multiplication performance on FPGAs”, Proc. International Conference    on Field Programmable Logic and Applications, pp. 305-310, September    2011.-   [43] J. Fowers, K. Ovtcharov, “A High Memory Bandwidth FPGA    Accelerator for Sparse Matrix-Vector Multiplication”, Proc. IEEE    22nd International Symposium on Field-Programmable Custom Computing    Machines. pp 36-43, May 2014.-   [41] Z. Jovanovic, V. Milutinovic, “FPGA accelerator for    floating-point matrix multiplication”, IET Computers & Digital    Techniques, 6(4): 249-256.

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1. An ultrasound imaging system comprising: an array of ultrasoundtransducer elements that send ultrasound energy into an object whenenergized for respective transmission time periods and provide responsesto ultrasound energy emitted from the object for respective receptiontime periods; a reception modulation circuit modulating the responseswith irregular sequences of modulation coefficients; a combiner circuitcombining the modulated responses; and an image reconstruction processorconfigured to computer-process the combined modulated responses into oneor more images of the object.
 2. The system of claim 1, in which thecombiner circuit is configured to combine the modulated responses in theanalog domain.
 3. The system of claim 1, in which the combiner circuitcomprises at least two combiner channels each combining a respectivesubset of the responses.
 4. The system of claim 1, in which thereception modulation circuit is configured to modulate the response witha sequence of pseudo-random modulation coefficients.
 5. The system ofclaim 1, in which the reception modulation circuit is configured tomodulate the response with coefficients related to columns of Hadamardmatrices.
 6. The system of claim 1, further including a transmissionmodulation circuit configured to select for energizing in eachtransmission period only plural-element subsets of the transducerelements, which subsets differ between transmission time periods.
 7. Thesystem of claim 1, in which the modulation circuit is configured toenergize only pseudo-randomly selected different subsets of thetransducer elements for different transmission time periods.
 8. Thesystem of claim 1, in which the modulation circuit is configured tomodulate the responses with waveforms of positive and negative levels.9. The system of claim 8, in which the combiner circuit comprises atleast one amplifier having a positive input receiving the portions ofthe responses modulated with the positive levels and a negative inputreceiving the portions of the responses modulated with the negativelevels of the modulating waveforms.
 10. The system of claim 1, in whichthe reconstruction processor is configured to apply an imaging matrix tothe combined modulated responses to thereby generate the one or moreimages of the object.
 11. An ultrasound imaging system comprising: amulti-element set of ultrasound transducer elements; an excitation pulsegenerator providing a succession of excitation pulses to the transducerelements; a receiving switch matrix modulating echoes received by thetransducer elements in response to the excitation pulses applied to anobject, with an essentially random sequence of modulation coefficients;a circuit summing the modulated echoes in the analog domain; and animage reconstruction processor configured to computer-process the summedmodulated echoes into one or more images of the object.
 12. The systemof claim 11, in which the receiving switch matrix modulates the echoeswith modulating waveforms having irregular periods.
 13. The system ofclaim 12, in which the modulating waveforms comprise waveforms of asuccession of positive and negative levels.
 14. The system of claim 13,including a differential charge amplifier, wherein the echoes modulatedwith the positive levels are supplied to a positive input and the echoesmodulated with the negative levels are supplied to a negative input ofthe differential amplifier.
 15. The system of claim 11, in which theimage reconstruction processor is configured to apply an image matrix tothe summed modulated echoes to generate an image of the object.
 16. Thesystem of claim 15, in which the image matrix is selected to relatesummed echoes from a known object to an expected image of the objectgenerated with the image reconstruction processor.
 17. The system ofclaim 11, including an analog-to-digital converter (ADC) converting thesummed echoes into a digital sequence supplied to the imagereconstruction processor.
 18. The system of claim 11, further includinga transmission switch matrix transmitting each excitation pulse only toa respective, essentially randomly selected subset of the elements inthe set.
 19. An ultrasound imaging system having an echo-signalreceiving chain comprising: an array containing a total of L acoustictransducer elements configured to receive echo acoustic pressure wavesfrom an imaged target and convert the received pressure waves toelectrical signals, where L is a positive integer greater than one; aswitch matrix configured to modulate the electrical signals from thetransducer elements and supply the modulated signals to one or moresummation nodes; one or more amplifiers performing summation andamplification of the modulated echo signals from the switch matrixsummed at the summation nodes; an analog-to-digital converter configuredto convert an output signal from the one or more amplifiers to digitalform; and an image reconstruction module configured to reconstruct anultrasound image of the target from an output of the analog-to-digitalconverter according to a reconstruction algorithm.
 20. The ultrasoundimaging system of claim 19, in which the switch matrix is configured tochange the polarity of the received echo signals by multiplying theelectrical signals from the transducer elements with modulationcoefficients equal to 1 or −1.
 21. The ultrasound imaging system ofclaim 20, in which the modulation coefficients are changed over N timesamples during a single echo-signal receive operation, where N is aninteger greater than one.
 22. The ultrasound imaging system of claim 21,in which the modulation coefficients are a total of N modulationcoefficients for each of the L elements of the array, where N is aninteger greater than one, and are changed in a pseudo-random manner. 23.The ultrasound imaging system of claim 21, in which the modulationcoefficients associated to one element of the transducer array areelements of columns of N×N Hadamard matrix, where N is an integergreater than one.
 24. The ultrasound imaging system of claim 20, inwhich the modulation coefficients are changed over N time samples andacross all or some of the elements of the transducer array during asingle echo-signal receive operation, where N is a positive integergreater than one.
 25. The ultrasound imaging system of claim 24, inwhich the modulation coefficients across different elements of thetransducer array are changed in a pseudo-random manner.
 26. Theultrasound imaging system of claim 24, in which the modulationcoefficients over time and across different elements of the transducerarray correspond to an N×L submatrix of a N×N Hadamard matrix H obtainedby removing some columns of the matrix H.
 27. The ultrasound imagingsystem of claim 19, in which the image reconstruction module uses aleast-squares estimation algorithm to estimate the image of the target.28. The ultrasound imaging system of claim 19, in which the imagereconstruction module operates an image reconstruction algorithmutilizing sparsity of signals for improved imaging resolution.
 29. Theultrasound imaging system of claim 19, in which the image reconstructionmodule comprises one or more remote image reconstruction modules. 30.The ultrasound imaging system of claim 19, in which the imagereconstruction module utilizes an image reconstruction algorithmallowing trade-off between computational complexity and reconstructedimage quality.
 31. The ultrasound imaging system of claim 19, in whichthe image reconstruction module comprises hardware computing elementsconfigured to carry out image reconstruction allowing dynamicreconfiguration.
 32. The ultrasound imaging system of claim 19, in whichthe elements of the transducer array are configured to generate the sameacoustic pulse resulting in a plane wave excitation during a single ormultiple acoustic pressure wave transmissions.
 33. The ultrasoundimaging system of claim 19, in which the transducer array is configuredto use only a subset of elements of the transducer array to generate thesame acoustic pulse during a single or multiple acoustic pressure wavetransmissions.
 34. The ultrasound imaging system of claim 33, in whichthe subset of elements of the transducer array is chosen in apseudo-random manner for each of acoustic pressure wave transmission.35. The ultrasound imaging system of claim 19, in which the transducerarray is configured with one subset of the elements generating the sameacoustic pulse and a disjoint subset generating the same but invertedacoustic pulse during a single or multiple acoustic pressure wavetransmissions.
 36. The ultrasound imaging system of claim 35, in whichthe two subsets of elements of the transducer array are chosen in apseudo-random manner for each of the acoustic pressure wavetransmissions.
 37. An ultrasound imaging system having an echo-signalreceiving chain that comprises: an array containing a total of Lacoustic transducer elements that receive an echo acoustic pressure wavefrom an imaged target and convert the received pressure wave toelectrical echo signals, where L is an integer greater than one; aswitch matrix configured to select two or more disjoint subsets of theelements of the transducer array and to connect the subsets to differentsummation nodes; an amplifier associated to each of the summation nodesand configured to perform echo signal summation and amplification; ananalog-to-digital converter converting an output signal from each of theamplifiers to digital form; and an image reconstruction moduleconfigured to operate according to a reconstruction algorithm thatreconstructs an ultrasound image of the target from outputs of theanalog-to-digital converters.
 38. The ultrasound imaging system of claim37, in which the analog-to-digital converter comprises two or moreanalog-to-digital converters each associated with a respective one ofthe amplifiers.
 39. The ultrasound imaging system of claim 37, in whichthe switch matrix is configured to select the subsets of elements of thetransducer array in a pseudo-random manner.
 40. The ultrasound imagingsystem of claim 37, in which the switch matrix is configured to changethe subsets of elements of the transducer array over N time samples,where N is an integer greater than one.
 41. The ultrasound imagingsystem of claim 37, in which the switch matrix is configured to performecho-signal modulation in addition to selecting disjoint subsets ofelements of the transducer array.
 42. The ultrasound imaging system ofclaim 37, in which the image reconstruction module is configured tooperate in accordance with a reconstruction algorithm utilizing aleast-squares estimation method to estimate the image of the target. 43.The ultrasound imaging system of claim 37, in which the imagereconstruction module operates in accordance with a reconstructionalgorithm utilizing signal sparsity for improved imaging resolution. 44.The ultrasound imaging system of claim 37, in which the imagereconstruction module comprises remote image reconstruction equipment.45. The ultrasound imaging system of claim 37, in which the imagereconstruction module operates in accordance with a reconstructionalgorithm that allows trade-off between computational complexity andreconstructed image quality.
 46. The ultrasound imaging system of claim37, in which the reconstruction module comprises hardware computingelements that carry out the image reconstruction allowing dynamicreconfiguration.
 47. The ultrasound imaging system of claim 37, in whichthe elements of the transducer array are configured to generate the sameacoustic pulse resulting in a plane wave excitation during a single ormultiple acoustic pressure wave transmissions.
 48. The ultrasoundimaging system of claim 37, in which only a subset of the elements ofthe transducer array generate the same acoustic pulse during a single ormultiple acoustic pressure wave transmissions.
 49. The ultrasoundimaging system of claim 48, in which the subset of elements of thetransducer array is chosen in a pseudo-random manner for each ofacoustic pressure wave transmission.
 50. The ultrasound imaging systemof claim 37, in which one subset of elements of the transducer arraygenerates the same acoustic pulse and a disjoint subset generating thesame but inverted acoustic pulse during a single or multiple acousticpressure wave transmissions.
 51. The ultrasound imaging system of claim50, in which two subsets of elements of the transducer array areselected in a pseudo-random manner for each acoustic pressure wavetransmission.
 52. An ultrasound imaging system having an acousticwaveform transmission chain that comprises: a digital-to-analogconverter configured to convert a digital excitation waveform to analogform; a power amplifier configured to amplify an output signal from thedigital-to-analog converter; a switch matrix configured to receive theamplified signal, pseudo-randomly select only a subset of the elementsof the transducer array during a single acoustic pressure wavetransmission, and connect only the elements of the subset to the outputof the power amplifier; and an array of a total of L acoustic transducerelements that receive electric signals from the switch matrix andconvert the received electrical signals to acoustic pressure wave, whereL is an integer greater than one.
 53. An ultrasound imaging methodcomprising: sending ultrasound energy into an object from an array ofultrasound transducer elements and receiving responses to ultrasoundenergy emitted from the object for with said array; modulating theresponses with irregular sequences of modulation coefficients; combiningthe modulated responses in the analog domain; and computer-processingthe combined modulated responses into one or more images of the object.54. The method of claim 54, including combining modulated responses arecombined in at least two combiner channels each combining a respectivesubset of the responses.
 55. The method of claim 54, includingconfiguring the reception modulation circuit to modulate the responsewith a sequence of pseudo-random modulation coefficients.
 56. The methodof claim 54, including configuring the array of transducers as aone-dimensional array but processing the modulated responses astwo-dimensional images of a three-dimensional object.
 57. The method ofclaim 54, including using a two-dimensional array of transducers in thesending step.